{
  "id": "2001.10725",
  "version": "v1",
  "published": "2020-01-29T08:39:46.000Z",
  "updated": "2020-01-29T08:39:46.000Z",
  "title": "Linear repetitivity beyond abelian groups",
  "authors": [
    "Siegfried Beckus",
    "Tobias Hartnick",
    "Felix Pogorzelski"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "We show that linearly repetitive Delone sets in Heisenberg groups have a uniquely ergodic hull. More generally we establish unique ergodicity of hulls of weighted Delone sets in amenable unimodular lcsc groups under a new repetitivity condition which we call tempered repetitivity, and which coincides with linear repetitivity for certain metrics on groups of polynomial growth. Our proof is based on a new general sub-additive convergence theorem, which also has applications concerning the existence of certain Banach densities and uniform approximation of the spectral distribution function of finite hopping range operators on Cayley graphs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-01-29T08:39:46.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "linear repetitivity",
      "abelian groups",
      "amenable unimodular lcsc groups",
      "general sub-additive convergence theorem",
      "spectral distribution function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}